Question

4) Calcule a divisões abaixo: a) 2i / 3 + i b) 5 + 1 / 1 – i

Answer 1

Resposta:

a)

$\frac{5}{3} i$

b)

$6 - i$

Answer 2

Explicação passo-a-passo:

a) $\sf \dfrac{2i}{3+i}=\dfrac{2i}{3+i}\cdot\dfrac{3-i}{3-i}$

$\sf \dfrac{2i}{3+i}=\dfrac{6i-2i^2}{3^2-i^2}$

$\sf \dfrac{2i}{3+i}=\dfrac{6i-2\cdot(-1)}{9-(-1)}$

$\sf \dfrac{2i}{3+i}=\dfrac{2+6i}{9+1}$

$\sf \dfrac{2i}{3+i}=\dfrac{2+6i}{10}$

$\sf \dfrac{2i}{3+i}=\dfrac{1}{5}+\dfrac{3i}{5}$

b) $\sf \dfrac{5+i}{1-i}=\dfrac{5+i}{1-i}\cdot\dfrac{1+i}{1+i}$

$\sf \dfrac{5+i}{1-i}=\dfrac{5+i+5i+i^2}{1^2-i^2}$

$\sf \dfrac{5+i}{1-i}=\dfrac{5+i+5i-1}{1-(-1)}$

$\sf \dfrac{5+i}{1-i}=\dfrac{4+6i}{1+1}$

$\sf \dfrac{5+i}{1-i}=\dfrac{4+6i}{2}$

$\sf \dfrac{5+i}{1-i}=2+3i$